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Does the shape of the curve, that is produced in space by a mass, have a name ? 
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#1
Sep1807, 06:24 AM

P: 2

I have been reading an article about a theory of gravity that involves space being curved or warped.
An example was given where a heavy weight, representing the sun, is placed in the centre of a trampoline, and a golf ball, representing the earth, is caused to circle the centre of the trampoline due to the depression caused by the heavy weight. I have two questions I would like to ask. 1) What is the name given to the shape of the curve that is produced in space by a mass ? I remember studying Conic Sections when I was at school and just as you can derive many different parabolic curves from one cone, they are all called a parabola. Equally, although different masses will cause different curvatures of space, I presume that all these curves will come under just one name. Just as I am able to understand the relationship between a parabola and a cone, my wish is to look up the definition of this name in order to understand what the underlying relationship of the curve is. ( I understand that space can be looked upon as being a three dimensional surface curved through four dimensional space. This is analogous to the two dimensional surface of the trampoline being curved through three dimensional space. ) 2) At what point, and how, does the trampoline analogy break down ? My understanding, from the article, is that the direction that the earth takes in space, is completely controlled by the curvature of the space itself. I can certainly understand that the curvature will influence the direction the Earth takes but not control it. From the trampoline example, there are essentially two things controlling the direction of the golf ball. One is the curvature of the trampoline and the other ( ignoring friction ) is the force of gravity acting downwards on the ball. However, as far as I can see, there is no equivalent in the SunEarth system to gravity acting downwards on the golf ball. If we imagine our three dimensional universe to be the three dimensional surface of a four dimensional sphere then, to continue the analogy with the trampoline, the force of gravity acting on the golf ball would be equivalent to a force acting on matter towards the centre of the four dimensional sphere. Thus, this force pulls the Earth down into the depression caused by the Sun and the Sun is also pulled on by this force. The implication, from the article, is that the direction that the earth takes in space, is completely controlled by the curvature of the space that the earth travels through. How can this be ? ( Perhaps I should note here that I may be having difficulty with the fact that the depression in the surface of the trampoline is negatively curved. Certainly, if we were dealing with a positively curved surface, ie. a sphere around the sun that the Earth travelled on, then there would be no doubt that the Earth would be forced to orbit the Sun on a geodesic.) I apologise about being so long winded with my questions. However, my feeling is that, if I am able to articulate where my thinking lies, then you will more easily be able to comment on my misunderstandings and point me to where I can do further reading. I hope I have chosen the correct forum to post to and I hope my questions aren’t too basic for this forum. 


#2
Sep1807, 07:06 AM

P: 4

"However, as far as I
can see, there is no equivalent in the SunEarth system to gravity acting downwards on the golf ball." This is where the analogy breaks down: at the first step. A better analogy can be found in TaylorWheeler's Spacetime Physics, two men walkig along meridians of Earth. Do you have this? m 


#3
Sep1807, 07:14 AM

P: 4,058

The trampoline is an analogy for curved space. But you need curved spacetime to understand how gravitation works. Try this:
http://fy.chalmers.se/~rico/Theses/tesx.pdf http://www.adamtoons.de/physics/gravitation.swf 


#4
Sep1907, 07:18 AM

P: 2

Does the shape of the curve, that is produced in space by a mass, have a name ?
Thank you mutant and A.T.for your replies.
No, I have never heard of TaylorWheeler's Spacetime Physics but a Google search shows it to be well recommended Gravity Illustrated Spacetime Edition also seems to be ideal if I can cope with a Doctoral Thesis. You have both let me know I should be reading about spacetime and I am very greatful to know this. By the way, A.T.’s link http://www.adamtoons.de/physics/gravitation.swf just brings up a Black ( and I do mean Black and not blank ) page. It does this in both Mozilla and Internet Explorer. I am very interested to see what the link contains. I went to http://www.adamtoons.de/ and found it contains the link http://www.adamtoons.de/physics/gravitation.swf so I presume I don’t have a plugin. I was wondering if A.T. could please suggest what I can do to view the page. 


#5
Sep1907, 08:52 AM

P: 4,058

http://www.adobe.com/products/flashplayer/ Some browsers are also blocking active content depending on security settings. 


#6
Sep1907, 09:30 AM

P: 31

I thought gravity was the curve produced in spacetime...



#7
Sep1907, 01:41 PM

Emeritus
Sci Advisor
P: 7,633

Yes, gravity requires a curved spacetime, not just "curved space". In fact, with the usual slicing of spacetime into space+time, the curvature in the space part is present but negligible at ordinary velocities  it is the nonspatial curvature that is important.
(This result can vary with different ways of "slicing" spacetime, but the usual Schwarzschild coordinate time acts in this manner). 


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